snap objects of same topology together by vertex index
I don't think there is something about that except Python.
This script will report vertex coordinates of active object to all the selected objects.
Version 1
Just give object the same topology:
import bpy

def snap_by_vertex_index(obj, target):
    for o, t in zip(obj.data.vertices, target.data.vertices):
        o.co = t.co
        

target = bpy.context.active_object

if target and target.type == 'MESH':
    objects = [o for o in bpy.context.selected_objects if o.type == 'MESH' and o is not target]
    for o in objects:
        snap_by_vertex_index(o, target)

Version 2
Or, as suggested @batFINGER in comments, that can be moving vertices to the target:
import bpy

def snap_by_vertex_index2(obj, target):
    mat = obj.matrix_world.inverted() @ target.matrix_world
    for o, t in zip(obj.data.vertices, target.data.vertices):
        o.co = mat @ t.co

target = bpy.context.active_object

if target and target.type == 'MESH':
    objects = [o for o in bpy.context.selected_objects if o.type == 'MESH' and o is not target]
    for o in objects:
        snap_by_vertex_index2(o, target)